Statement 1 :

If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change.

Statement 2 :

When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.

The potential energy of a particle of mass m is given by

$$\mathrm{U}(x)=\left\{\begin{array}{cc}\mathrm{E}_{0} & 0 \leq x \leq 1 \\ 0 & x>1\end{array}\right.$$

$$\lambda_{1}$$ and $$\lambda_{2}$$ are the de Broglie wavelengths of the particle, when $$0 \leq x \leq 1$$ and $$x > 1$$, respectively. If the total energy of particle is $$2 \mathrm{E}_{0}$$, find $$\frac{\lambda_{1}}{\lambda_{2}}$$.